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001 978-3-662-63207-9
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020 _a9783662632079
_9978-3-662-63207-9
024 7 _a10.1007/978-3-662-63207-9
_2doi
050 4 _aTA329-348
050 4 _aTA345-345.5
072 7 _aTBJ
_2bicssc
072 7 _aTEC009000
_2bisacsh
072 7 _aTBJ
_2thema
082 0 4 _a620
_223
100 1 _aMorino, Luigi.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_950859
245 1 0 _aMathematics and Mechanics - The Interplay
_h[electronic resource] :
_bVolume I: The Basics /
_cby Luigi Morino.
250 _a1st ed. 2021.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2021.
300 _aXXXVI, 1019 p. 200 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPart I The beginning - Precalculus -- Part II Calculus and dynamics of a particle in one dimension -- Part III Multivariate calculus and mechanics in three dimensions.
520 _aMathematics plays an important role in mechanics and other human endeavours. Validating examples in this first volume include, for instance: the connection between the golden ratio (the “divine proportion" used by Phidias and many other artists and enshrined in Leonardo's Vitruvian Man, shown on the front cover), and the Fibonacci spiral (observable in botany, e.g., in the placement of sunflower seeds); is the coast of Tuscany infinitely long?; the equal-time free fall of a feather and a lead ball in a vacuum; a simple diagnostic for changing your car's shocks; the Kepler laws of the planets; the dynamics of the Sun-Earth-Moon system; the tides' mechanism; the laws of friction and a wheel rolling down a partially icy slope; and many more. The style is colloquial. The emphasis is on intuition - lengthy but intuitive proofs are preferred to simple non-intuitive ones. The mathematical/mechanical sophistication gradually increases, making the volume widely accessible. Intuition is not at the expense of rigor. Except for grammar-school material, every statement that is later used is rigorously proven. Guidelines that facilitate the reading of the book are presented. The interplay between mathematics and mechanics is presented within a historical context, to show that often mechanics stimulated mathematical developments - Newton comes to mind. Sometimes mathematics was introduced independently of its mechanics applications, such as the absolute calculus for Einstein's general theory of relativity. Bio-sketches of all the scientists encountered are included and show that many of them dealt with both mathematics and mechanics.
650 0 _aEngineering mathematics.
_93254
650 0 _aEngineering—Data processing.
_931556
650 0 _aMechanics, Applied.
_93253
650 0 _aMathematical physics.
_911013
650 0 _aMechanics.
_98758
650 1 4 _aMathematical and Computational Engineering Applications.
_931559
650 2 4 _aEngineering Mechanics.
_931830
650 2 4 _aMathematical Physics.
_911013
650 2 4 _aClassical Mechanics.
_931661
710 2 _aSpringerLink (Online service)
_950860
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783662632055
776 0 8 _iPrinted edition:
_z9783662632062
856 4 0 _uhttps://doi.org/10.1007/978-3-662-63207-9
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cEBK
999 _c78664
_d78664